Tomlinson-Harashima precoding (TH preceding) is a transmitter equalization technique where equalization is performed at the transmitter side, and has been widely used in many communication systems. It can eliminate error propagation and allows use of capacity-achieving channel codes, such as low-density parity-check (LDPC) codes, in a natural way.
Recently, TH precoding has been proposed to be used in 10 Gigabit Ethernet over copper (10GBASE-T). The symbol rate of 10GBASE-T is 800 Mega Baud. However, a TH precoder contains feedback loops, and it may be impossible to clock the straightforward implementation of the TH precoder at such high speed. Thus, high speed design of TH precoders is of great interest.
How to design a fast TH precoder is a challenging task. The architecture of a TH precoder is similar to that of a DFE (decision feedback equalizer). The only difference is that a quantizer in the DFE is replaced with a modulo device in the TH precoder. In a PAM-M (M-level pulse amplitude modulation) system, the number of different outputs of the quantizer in the DFE is finite, which is usually equal to the size of the symbol alphabet, i.e., M. However, theoretically, the number of different outputs of the modulo device in the TH precoder is infinite for a floating-point implementation. For a fixed-point implementation, it is exponential with the wordlength. In some applications, the wordlength can be very large. Thus, many known techniques exploiting the property of finite-level outputs of the nonlinear element in the DFE, such as the pre-computation technique (See, e.g., in K. K. Parhi, “Pipelining in algorithms with quantizer loops,” IEEE Trans. on Circuits and Systems, vol. 37, no. 7, pp. 745-754, July 1991), cannot be directly applied to pipeline the TH precoder. Furthermore, the use of look-ahead techniques in the TH precoder, such as those for pipelining IIR filters (See, e.g., K. K. Parhi and D. G. Messerschmitt, “Pipeline interleaving and parallelism in recursive digital filters, Part I and Part II,” IEEE Trans. Acoust., Speech, Signal Processing, pp. 1099-1135, July 1989), is not straightforward as the TH precoder contains nonlinear elements in its feedback loops.
What is needed is a fast TH precoder and a method for designing the same, which can fully exploit the properties of a TH precoder.